高维数据局部贝叶斯网络结构学习

doi:10.12305/j.issn.1001-506X.2024.08.15

Abstract

Abstract:

To address the issue of low learning accuracy and efficiency of Bayesian network structure learning under high-dimensional data, a feature selection based on normalized mutual information and approximate Markov blanket (FSNMB) algorithm is proposed to obtain the Markov blanket (MB) of the target node. The MB and Meek's rule are further combined to implement the algorithm of construct local Bayesian network based on feature selection (FSCLBN), which improves the accuracy and efficiency of local Bayesian network structure learning. Experiment results show that in high-dimensional data, the FSCLBN algorithm has more advantages than the existing local Bayesian network structure learning algorithms.

Key words: Bayesian network, feature selection, mutual information, Markov blanket (MB)

CLC Number:

TP181

Yangyang WANG, Xiaoguang GAO, Xinxin RU. Local Bayesian network structure learning for high-dimensional data[J]. Systems Engineering and Electronics, 2024, 46(8): 2676-2685.

Figures/Tables 12

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References 31

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标准网络	节点数量	边数量	最大入度	最大出度
Alarm	37	46	4	5
Hepar2	70	123	6	17
Win95pts	76	112	5	10
Pathfinder	109	195	5	106
Andes	223	338	6	12

节点序号	所属网络	PC和配偶节点数量
35	Alarm	1, 4, 3
19	Hepar2	2, 17, 7
31	Win95pts	0, 10, 19
1	Pathfinder	0, 106, 30
163	Andes	2, 6, 9

数据集	样本数量	特征数量	分类数量
Wine	178	14	3
Breast	569	30	2
Ionosphere	351	34	2
Splice	3 175	60	3
Semeion	1 593	256	10

数据集	算法	F得分	准确率	召回率	运行耗时/s
Alarm	FSNMB	0.57±0.07	0.44±0.08	0.79±0.06	0.01±0.01
	IAMB	0.22±0.00^*	1.00±0.00	0.13±0.00	0.00±0.00
	HITON-MB	0.53±0.07	0.36±0.07	0.98±0.05	0.13±0.11
	MMMB	0.40±0.02^*	0.25±0.02	0.98±0.05	2.48±0.44
	STMB	0.36±0.00^*	0.22±0.00	1.00±0.00	0.57±0.35
Hepar2	FSNMB	0.43±0.10	0.34±0.08	0.61±0.16	0.01±0.01
	IAMB	0.07±0.02^*	0.90±0.30	0.04±0.01	0.00±0.00
	HITON-MB	0.38±0.13^*	0.46±0.15	0.33±0.12	0.01±0.01
	MMMB	0.52±0.05	0.42±0.04	0.67±0.07	0.72±0.15
	STMB	0.53±0.00^*	0.36±0.00	1.00±0.00	0.94±0.40
Win95pts	FSNMB	0.33±0.01	0.75±0.02	0.21±0.01	0.01±0.00
	IAMB	0.00±0.01^*	0.02±0.14	0.00±0.00	0.00±0.00
	HITON-MB	0.12±0.01^*	0.67±0.05	0.07±0.02	0.01±0.00
	MMMB	0.12±0.01^*	0.51±0.07	0.07±0.00	0.01±0.00
	STMB	0.32±0.01	0.28±0.01	0.37±0.02	0.01±0.00
Pathfinder	FSNMB	0.66±0.04	1.00±0.00	0.50±0.05	4.03±1.38
	IAMB	0.00±0.00^*	0.00±0.00	0.00±0.00	0.00±0.00
	HITON-MB	0.00±0.00^*	0.00±0.00	0.00±0.00	0.00±0.00
	MMMB	1.00±0.00^*	0.99±0.00	1.00±0.00	67.57±0.30
	STMB	-	-	-	-
Andes	FSNMB	0.34±0.07	0.30±0.06	0.41±0.11	0.04±0.02
	IAMB	0.14±0.05^*	0.65±0.24	0.08±0.03	0.01±0.00
	HITON-MB	0.26±0.08^*	0.49±0.14	0.18±0.06	0.01±0.00
	MMMB	0.23±0.07^*	0.44±0.13	0.16±0.05	0.02±0.00
	STMB	0.27±0.08	0.19±0.06	0.46±0.17	0.01±0.01

数据集	算法	F得分	准确率	召回率	运行耗时/s
Alarm	FSNMB	0.95±0.06	0.96±0.06	0.94±0.09	0.00±0.00
	IAMB	0.55±0.00^*	1.00±0.00	0.38±0.00	0.00±0.00
	HITON-MB	0.94±0.06	0.95±0.06	0.93±0.09	0.01±0.00
	MMMB	0.94±0.06	0.95±0.06	0.93±0.09	0.01±0.00
	STMB	0.58±0.08^*	0.41±0.08	0.99±0.04	0.01±0.00
Hepar2	FSNMB	0.47±0.08	0.93±0.09	0.32±0.07	0.01±0.00
	IAMB	0.27±0.03^*	0.90±0.11	0.16±0.02	0.01±0.00
	HITON-MB	0.33±0.07^*	0.96±0.09	0.20±0.05	0.01±0.00
	MMMB	0.32±0.07^*	0.96±0.09	0.20±0.05	0.01±0.00
	STMB	0.47±0.11	0.61±0.11	0.40±0.12	0.02±0.01
Win95pts	FSNMB	0.47±0.00	1.00±0.02	0.31±0.00	0.01±0.00
	IAMB	0.24±0.01^*	0.80±0.01	0.14±0.00	0.01±0.00
	HITON-MB	0.32±0.01^*	0.75±0.00	0.21±0.02	0.02±0.01
	MMMB	0.33±0.03^*	0.86±0.02	0.21±0.04	0.01±0.01
	STMB	0.45±0.05	0.55±0.05	0.38±0.04	0.02±0.01
Pathfinder	FSNMB	0.70±0.02	1.00±0.00	0.53±0.02	3.95±0.63
	IAMB	0.00±0.00^*	0.00±0.00	0.00±0.00	0.00±0.00
	HITON-MB	0.00±0.00^*	0.00±0.00	0.00±0.00	0.00±0.00
	MMMB	1.00±0.00^*	0.99±0.00	1.00±0.00	370.90±84.60
	STMB	-	-	-	-
Andes	FSNMB	0.75±0.05	0.94±0.07	0.63±0.06	0.03±0.01
	IAMB	0.45±0.03^*	0.98±0.06	0.29±0.02	0.02±0.00
	HITON-MB	0.74±0.05	0.92±0.06	0.62±0.07	0.04±0.01
	MMMB	0.75±0.07	0.90±0.08	0.65±0.09	0.04±0.01
	STMB	0.37±0.04^*	0.24±0.03	0.77±0.08	0.10±0.03

Local Bayesian network structure learning for high-dimensional data

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数据集	算法	各分类器分类精度					平均分类精度
数据集	算法	KNN	SVM	RF	DT	NBC	平均分类精度
Wine	FSNMB	0.95	0.97	0.94	0.85	0.97	0.94
	IAMB	0.77	0.77	0.77	0.77	0.77	0.77
	HITON-MB	0.94	0.98	0.94	0.89	0.97	0.94
	MMMB	0.95	0.98	0.95	0.88	0.97	0.95
	STMB	0.94	0.98	0.94	0.89	0.97	0.94
Breast	FSNMB	0.94	0.94	0.95	0.93	0.63	0.88
	IAMB	0.92	0.92	0.91	0.91	0.92	0.91
	HITON-MB	0.95	0.96	0.94	0.94	0.63	0.88
	MMMB	0.95	0.96	0.94	0.93	0.63	0.88
	STMB	0.95	0.96	0.94	0.92	0.63	0.88
Ionosphere	FSNMB	0.85	0.93	0.92	0.92	0.64	0.85
	IAMB	0.88	0.88	0.88	0.88	0.64	0.83
	HITON-MB	0.83	0.94	0.95	0.90	0.64	0.85
	MMMB	0.83	0.93	0.94	0.93	0.64	0.86
	STMB	0.83	0.94	0.93	0.92	0.64	0.85
Splice	FSNMB	0.83	0.93	0.95	0.93	0.85	0.90
	IAMB	0.80	0.81	0.81	0.81	0.74	0.80
	HITON-MB	0.71	0.90	0.94	0.93	0.89	0.88
	MMMB	0.73	0.90	0.94	0.92	0.89	0.88
	STMB	0.72	0.90	0.94	0.93	0.90	0.88
Semeion	FSNMB	0.87	0.91	0.89	0.68	0.17	0.70
	IAMB	0.38	0.41	0.40	0.41	0.33	0.39
	HITON-MB	-	-	-	-	-	-
	MMMB	-	-	-	-	-	-
	STMB	-	-	-	-	-	-

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数据集	算法	F得分	准确率	召回率	运行耗时/s
Alarm	FSNMB	0.99±0.05	1.00±0.00	0.98±0.08	0.03±0.00
	IAMB	0.80±0.05^*	1.00±0.00	0.68±0.06	0.01±0.00
	HITON-MB	0.99±0.02	0.99±0.04	1.00±0.00	0.03±0.00
	MMMB	0.98±0.03	0.97±0.05	1.00±0.00	0.03±0.00
	STMB	0.65±0.05^*	0.49±0.06	1.00±0.00	0.05±0.00
Hepar2	FSNMB	0.55±0.03	1.00±0.00	0.38±0.03	0.07±0.01
	IAMB	0.41±0.03^*	0.97±0.06	0.26±0.02	0.04±0.00
	HITON-MB	0.70±0.04^*	0.96±0.03	0.56±0.05	0.31±0.07
	MMMB	0.70±0.04^*	0.97±0.04	0.55±0.04	0.32±0.08
	STMB	0.68±0.04^*	0.52±0.03	0.79±0.06	1.22±0.32
Win95pts	FSNMB	0.58±0.01	0.81±0.00	0.45±0.01	0.12±0.00
	IAMB	0.38±0.01^*	0.88±0.01	0.24±0.00	0.05±0.00
	HITON-MB	0.71±0.01^*	0.89±0.01	0.59±0.01	0.15±0.01
	MMMB	0.78±0.00^*	0.95±0.01	0.66±0.01	0.18±0.00
	STMB	0.57±0.01	0.46±0.01	0.76±0.00	0.58±0.01
Pathfinder	FSNMB	0.72±0.02	1.00±0.00	0.57±0.03	4.81±0.41
	IAMB	0.03±0.01^*	1.00±0.00	0.02±0.00	0.01±0.00
	HITON-MB	0.87±0.01	1.00±0.01	0.77±0.02	244.8±26.70
	MMMB	0.98±0.01^*	0.99±0.00	0.97±0.02	416.3±22.51
	STMB	-	-	-	-
Andes	FSNMB	0.70±0.03	0.98±0.04	0.54±0.04	0.15±0.00
	IAMB	0.64±0.00	1.00±0.00	0.47±0.00	0.15±0.00
	HITON-MB	0.86±0.03^*	0.97±0.04	0.78±0.02	0.15±0.00
	MMMB	0.87±0.02^*	0.98±0.03	0.78±0.02	0.14±0.00
	STMB	0.35±0.02^*	0.21±0.01	0.89±0.03	0.42±0.03

数据集	算法	F得分	汉明距离	反向边数量	丢失边数量	多余边数量	运行耗时/s
Alarm	FSCLBN	0.58±0.15	3.60±1.65	0.50±0.53	1.60±0.70	1.40±1.43	0.01±0.01
	PCD_by_PCD	0.38±0.19^*	10.60±3.66	1.40±1.71	0.10±0.32	9.00±2.62	2.55±0.63
	CMB	0.23±0.23^*	6.20±2.78	3.60±1.26	0.10±0.32	2.50±2.27	0.42±0.42
	MB_by_MB	0.00±0.00^*	5.00±0.00	0.00±0.00	4.00±0.00	0.00±0.00	0.01±0.01
Hepar2	FSCLBN	0.31±0.11	19.80±2.86	1.30±0.48	12.90±1.97	5.60±2.67	0.03±0.02
	PCD_by_PCD	0.09±0.03^*	22.00±1.49	6.70±1.16	10.90±1.45	4.40±1.58	0.64±0.12
	CMB	0.11±0.03^*	20.00±1.49	2.80±1.23	14.80±1.55	2.40±1.58	0.02±0.01
	MB_by_MB	0.00±0.00^*	19.10±0.32	0.00±0.00	18.10±0.32	0.10±0.32	0.01±0.01
Win95pts	FSCLBN	0.41±0.20	8.50±1.43	0.50±0.71	6.10±1.66	1.90±1.37	0.01±0.01
	PCD_by_PCD	0.00±0.00^*	10.20±0.42	0.00±0.00	9.30±0.95	0.20±0.42	0.01±0.02
	CMB	0.00±0.00^*	10.20±0.42	0.00±0.00	9.00±0.94	0.20±0.42	0.01±0.02
	MB_by_MB	0.03±0.07^*	10.10±0.57	0.10±0.32	9.20±0.63	0.30±0.48	0.01±0.01
Andes	FSCLBN	0.17±0.10	15.30±3.02	0.40±0.52	6.00±1.12	8.90±2.38	0.06±0.03
	PCD_by_PCD	0.09±0.12^*	8.30±1.25	1.50±0.85	6.00±1.05	0.80±0.92	0.03±0.02
	CMB	0.11±0.15	9.30±1.20	1.50±0.97	5.80±0.92	2.00±0.82	0.17±0.15
	MB_by_MB	0.23±0.06	7.10±0.57	0.40±0.52	6.50±0.53	0.20±0.42	0.02±0.01

数据集	算法	F得分	汉明距离	反向边数量	丢失边数量	多余边数量	运行耗时/s
Alarm	FSCLBN	0.76±0.24	1.60±1.35	0.70±0.95	0.70±0.48	0.20±0.42	0.02±0.01
	PCD_by_PCD	0.79±0.15	1.30±0.67	0.40±0.84	0.60±0.52	0.00±0.00	0.02±0.01
	CMB	0.73±0.36	1.50±1.78	0.90±1.45	0.60±0.52	0.00±0.00	0.02±0.01
	MB_by_MB	0.58±0.23	3.20±1.40	0.50±0.71	1.90±0.74	0.80±0.63	0.01±0.01
Hepar2	FSCLBN	0.50±0.16	12.50±2.51	0.70±0.95	11.40±2.32	0.40±0.52	0.02±0.01
	PCD_by_PCD	0.20±0.10^*	16.60±1.17	2.60±1.35	14.00±1.05	0.00±0.00	0.01±0.00
	CMB	0.32±0.13^*	15.10±1.66	1.30±1.16	13.80±0.92	0.00±0.00	0.03±0.02
	MB_by_MB	0.17±0.08^*	20.10±2.88	2.10±1.37	14.70±0.82	3.30±2.63	0.02±0.01
Win95pts	FSCLBN	0.60±0.12	5.80±1.55	0.70±0.48	4.30±0.95	0.80±0.63	0.02±0.00
	PCD_by_PCD	0.11±0.13^*	9.30±0.82	1.50±1.51	7.20±1.03	0.00±0.00	0.05±0.04
	CMB	0.32±0.12^*	8.10±1.29	1.20±0.79	6.60±1.35	0.30±0.67	0.04±0.01
	MB_by_MB	0.16±0.17^*	11.70±2.63	1.60±1.07	7.20±0.92	2.90±1.60	0.03±0.01
Andes	FSCLBN	0.64±0.19	4.60±2.59	0.60±0.52	2.80±1.14	1.20±1.48	0.04±0.02
	PCD_by_PCD	0.34±0.18^*	5.70±1.50	3.60±1.10	2.00±0.67	0.10±0.32	0.01±0.01
	CMB	0.63±0.15	4.00±1.25	1.20±0.92	2.20±0.63	0.60±0.70	0.12±0.06
	MB_by_MB	0.30±0.09^*	10.90±1.29	0.90±0.57	4.50±0.53	5.50±1.08	0.10±0.00

数据集	算法	F得分	汉明距离	反向边数量	丢失边数量	多余边数量	运行耗时/s
Alarm	FSCLBN	0.92±0.07	0.60±0.52	0.10±0.32	0.50±0.53	0.00±0.00	0.04±0.00
	PCD_by_PCD	0.86±0.10	0.70±0.48	0.70±0.48	0.00±0.00	0.00±0.00	0.05±0.01
	CMB	0.92±0.26	0.50±1.58	0.40±1.26	0.00±0.00	0.10±0.32	0.11±0.05
	MB_by_MB	0.41±0.15^*	6.30±2.41	1.50±0.71	1.00±0.00	3.80±1.81	0.09±0.01
Hepar2	FSCLBN	0.61±0.04	10.70±0.82	0.00±0.00	10.70±0.82	0.00±0.00	0.08±0.01
	PCD_by_PCD	0.17±0.07^*	16.40±1.07	9.40±1.51	7.00±0.67	0.00±0.00	0.30±0.06
	CMB	0.53±0.13^*	10.70±2.06	3.80±2.04	6.90±0.57	0.00±0.00	0.91±0.30
	MB_by_MB	0.13±0.03^*	24.90±2.18	7.40±1.07	9.30±0.95	8.20±2.04	0.25±0.01
Win95pts	FSCLBN	0.64±0.04	5.60±0.84	0.20±0.42	3.80±0.79	1.10±0.57	0.13±0.02
	PCD_by_PCD	0.55±0.18	5.20±1.62	2.50±1.84	2.60±0.84	0.00±0.00	0.21±0.10
	CMB	0.63±0.23	5.20±2.10	1.80±2.49	2.20±0.79	1.20±0.79	0.56±0.06
	MB_by_MB	0.23±0.10^*	17.60±3.17	3.40±0.97	3.50±0.97	10.70±2.54	0.37±0.04
Andes	FSCLBN	0.56±0.15	4.30±1.06	0.00±0.00	2.80±0.42	0.00±0.00	0.37±0.05
	PCD_by_PCD	0.87±0.11^*	1.30±0.67	0.30±0.67	1.00±0.00	0.00±0.00	0.14±0.00
	CMB	0.77±0.10^*	2.10±0.57	1.10±0.57	1.00±0.00	0.00±0.00	0.79±0.22
	MB_by_MB	0.33±0.01^*	1.20±0.42	0.20±0.42	1.00±0.00	0.00±0.00	1.30±0.01